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For a multiple regression model, all the variables have p-values below 0.05. The p value for the whole model is below 0.05 as well. When I checked for multicollinearity, I got VIFs below 5 for all the variables, but one of the condition indexes is above 30! Does this mean I have multicollinearity and I can't do multiple regression?

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  • $\begingroup$ Multicollinearity makes the effective size of your sample smaller than the actual size. This then yields increased standard errors and decreased statistical significance of the parameters. If there are no problems with large standard errors and insignificant regressors, I would not worry too much about multicollinearity. $\endgroup$ – Richard Hardy Mar 26 '15 at 14:02
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(Note that individual variables do not have a condition index. Condition indexes are for a group of variables.)

One thing to be aware of when forming or interpreting condition indexes is that you need to center your $X$ variables first. Then your intercept will be uncorrelated with the rest of your variables and the condition index will be a measure of the multicollinearity amongst your variables. If you don't do this (and I'm guessing you didn't), the resulting condition index can say that there is a great deal of multicollinearity amongst your variables, but it is actually only for the intercept, which is not generally of interest and cannot be avoided anyway. To get a sense of this, it may help to read my answer here: Why does the standard error of the intercept increase the further $\bar x$ is from 0?

At any rate, the effect of multicollinearity is basically just to increase the standard errors of your slopes, which reduces your power. Your variables are significant, so it seems unlikely that you have anything to worry about.

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